Preservation of MJ-singularities under general residual intersections

Let $A$ be a nonsingular variety, let $X\subset A$ be a closed subscheme, and let $Y$ be a general $t$-residual intersection of $X$ in the sense of the paper. The singularities MJ-canonical and MJ-log canonical are the Mather–Jacobian singularity conditions used for $X$ and $Y$. Residual-intersection conjecture. If $X$ is MJ-canonical (respectively, MJ-log canonical), then $Y$ is MJ-canonical (respectively, MJ-log canonical). This predicts that the relevant MJ-singularities are preserved when passing to a general residual intersection.